Scanning　electron　microscopes　(SEM)　and　transmission　electron　microscopes　(TEM)　were　employed　to　investigate　the　topologically　close-packed　(TCP)　phases　in　an　experimental　nickel　base　single　crystal　superalloy.　Orientation　relationships　between　P　phase　and　matrix　were　found　as　(010)(P)//(1　(1)　over　bar1)(gamma)　and　[201](P)//[110](gamma)　in　which　atomic　arrangement　of　P　phase　obtains　the　optimal　matching　with　that　of　gamma/gamma＇　matrix　and　the　semi-coherent　interface　forms,　achieving　the　lower　interface　energy.　The　elemental　composition,　atomic　arrangement　of　low　index　planes　and　the　atomic　attachment　of　P　phase　with　matrix　were　analyzed　in　detail　to　investigate　the　atomic　scale　structure　of　the　fast-growing　semi-coherent　interface　and　its　effects　on　precipitate　growth.　Finally,　the　nucleation　of　P　phase　was　discussed.